DSpace/Manakin Repository

JavaScript is disabled for your browser. Some features of this site may not work without it.

BEARdocs is currently undergoing a scheduled upgrade. We expect the upgrade to be completed no later than Monday, March 2nd, 2015. During this time you will be able to access existing documents, but will not be able to log in or submit new documents.

Abstract:

We investigated distribution free methods for testing covariate adjusted treatment
effects. Dodd and Pepe (2003) proposed a semiparametric logistic regression model for the area under the ROC curve (AUC). Their model was motivated by the observation that the commonly used non-parametric Mann-Whitney statistic is a non-parametric estimate of the AUC, where the AUC gives a measure of the separation between two density functions. Their result allows one to test hypotheses using distribution free methods when the covariates are discrete, however, the standard errors generated using standard GLM software were not correct since the Bernoulli data used in the Mann-Whitney statistic are correlated. They used bootstrapping to compute the standard errors. In Chapter 2, we present an analytical method for estimating the standard errors as an alternative to the bootstrap procedure. In Chapter 3, we present a new semiparametric beta regression model for the AUC. This was done by defining the response variable as the placement value of the treatment responses with respect to a placebo population. This model allows for both discrete and continuous covariate effects. In Chapter 4, we expand our model in two ways. The first is for a clinical trial with multiple treatments arms and a placebo. The second extension is for longitudinal or repeated measures data. These extensions are illustrated using both simulated and real data.